document.write( "Question 1023119: s(x) = 2x − 4 over x^2 + x − 2\r
\n" ); document.write( "\n" ); document.write( "State the domain and range. (Enter your answers using interval notation.) \n" ); document.write( "

Algebra.Com's Answer #638682 by robertb(5830) $\"\"$ $\"About$

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$\"%282x-4%29%2F%28x%5E2%2Bx-2%29+=+%282x-4%29%2F%28%28x-1%29%28x%2B2%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "==> Domain of s(x) is ( $\"-infinity\"$ , -2)u(-2,1)u(1, $\"infinity\"$ ).\r
\n" ); document.write( "\n" ); document.write( "To find the range of s(x), let $\"y+=+%282x-4%29%2F%28x%5E2%2Bx-2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "==> $\"yx%5E2%2Byx-2y+=+2x-4\"$
\n" ); document.write( "==> $\"yx%5E2%2B%28y-2%29x%2B%284-2y%29+=+0\"$ , a quadratic equation in x with coefficients in terms of y. For such expression to have real roots, the discriminant \r
\n" ); document.write( "\n" ); document.write( " $\"b%5E2+-+4ac+=+%28y-2%29%5E2+-+4y%284-2y%29+%3E=0\"$ \r
\n" ); document.write( "\n" ); document.write( "<==> $\"%28y-2%29%5E2+%2B8y%28y-2%29+%3E=0\"$
\n" ); document.write( "<==> $\"%28y-2%29%289y-2%29+%3E=0\"$ .
\n" ); document.write( "The solution to this inequality is the union ( $\"-infinity\"$ , 2/9]u[2, $\"infinity\"$ ) .\r
\n" ); document.write( "\n" ); document.write( "Incidentally this is also the range of s(x). \n" ); document.write( "

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